The flag and arms of Burgohondo (municipal website) are prescribed by a Decree adopted on 25 March 1999 by the Municipal Council, signed on 29 March 1999 by the Mayor and published on 12 April 1999 in the official gazette of Castilla y León, No. 163, pp. 10,138-10,139 (text).
The symbols are described as follows:

Flag: Quadrangular, blue and gold arranged in diagonal. In the
middle of the flag is placed the coat of arms of Burgohondo.Coat of arms: Divided into three quarters, 1. Or a church building
gray roofed gules, 2. Or nine bezants gray, 3. Azure a tree argent
fructed or a bridge and waves argent. The shield surmounted with a
Royal crown.

The symbols were designed by Lorenzo Gómez Gómez. On the arms, the first quarter shows the Burgohondo monastery, recalling its religious,
political and social influence on the history of the town. In the
second quarter, the nine bezants symbolize the nine settlements once
part of the Burgohondo Council. The lower part of the shield shows a
peach tree, the peaches from Burgohondo being of national fame, and
river Alberche, used for ages for crop watering, fishing and grain
milling, and today a main environmental resource.

The Royal Academy of History did not like at all the proposed symbols (Boletin de la Real Academia de la Historia, 2001, 198, 1: 178):

Nearly nothing in the description of the proposed coat of arms can
pass the most lenient examination. Not the "gray church
building" [edificación eclesiástica de gris], not the bezants argent [indeed "gray"] on a field or, not the tree vert on a field blue, not the most weird representation of the waves... The municipality should
commission a new project to someone with at least basic knowledge in
the matter [of heraldry]. The flag contains the rejected coat of arms,
and is therefore rejected, too.